MOTIVATION In the context of studying whole metabolic networks and their interaction with the environment, the following question arises: given a set of target metabolites T and a set of possible external source metabolites , which are the minimal subsets of that are able to produce all the metabolites in T. Such subsets are called the minimal precursor sets of T. The problem is then whether...

Let G = (V, E) be an undirected graph, and let B ⊆ V × V be a collection of vertex pairs. We give an incremental polynomial time algorithm to enumerate all minimal edge sets X ⊆ E such that every vertex pair (s, t) ∈ B is disconnected in (V, E r X), generalizing wellknown efficient algorithms for enumerating all minimal s-t cuts, for a given pair s, t ∈ V of vertices. We also present an increme...

Argumentation Johannes P. Wallner, Georg Weissenbacher, and Stefan Woltran Institute of Information Systems, Vienna University of Technology, Favoritenstraße 9-11, A-1040 Vienna, Austria Abstract. In the area of propositional satisfiability (SAT), tremendous progress has been made in the last decade. Today’s SAT technology covers not only the standard SAT problem, but also extensions thereof, s...

LetG = (V,E) be an undirected graph, and letB ⊆ V ×V be a collection of vertex pairs. We give an incremental polynomial time algorithm to enumerate all minimal edge sets X ⊆ E such that every vertex pair (s, t) ∈ B is disconnected in (V,ErX), generalizing well-known efficient algorithms for enumerating all minimal s-t cuts, for a given pair s, t ∈ V of vertices. We also present an incremental p...

a r t i c l e i n f o a b s t r a c t Keywords: Inconsistency measures Minimal inconsistent subsets Minimal unsatisfiable subformulae SAT Random SAT There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are defined in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or exp...

We construct an example of a quasi-o-minimal group without the Exchange Property. A structure hM;<;:::i is called quasi-o-minimal 1] if in any structure elementarily equivalent to it the deenable subsets are exactly the Boolean combinations of 0-deenable subsets and intervals. A complete theory T is said to have the Exchange Property if, for any model M of T and for any X M and b; c 2 M, if b 2...

The Stone-Čech compactification of the natural numbers βω (or equivalently, the space of ultrafilters on the subsets of ω) is a well-studied space with interesting properties. Replacing the subsets of ω by partitions of ω in the construction of the ultrafilter space gives non-homeomorphic spaces of partition ultrafilters corresponding to βω. We develop a general framework for spaces of this typ...

Let C be an n-dimensional integral box, and π be a monotone property defined over the elements of C. We consider the problems of incrementally generating jointly the families Fπ and Gπ of all minimal subsets satisfying property π and all maximal subsets not satisfying property π, when π is given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applicatio...